What about engineered prefinished floating hardwoods? Very cost effective for the result you get.
We've also seen some amazing painted concrete floors posted on Hometalk - try searching posts for painted concrete or painted floors. Our Hometalk paint experts might have some suggestions for removing the adhesive.

I know a lot of people here are critical of laminate floors (including myself at times), but they are an inexpensive option that works really well over concrete. They won't last a lifetime, but they are fairly durable and tough, and look really nice.

Jamie, where is the floor. Basement or grade level slab? Reason being there are several concerns about the materials that you would use for one and the other. Moisture is the issue at hand. So is comfort as well.
Also knowing what the room is also helpful as there are many types of flooring options but many have a special use and what works well in one area may become a disaster in another.
Last question. How big an area are you looking to cover?

There are adhesive removers specific to the type of glue. Check with a professional supplier of flooring products in your area for suggestions and chemical strippers. Don't cut the products and use them at their suggested density. Nothing is perfect. We have used Bean-e-Do which is soy bean based and a Green product. Not cheap, but you will be amazed at the power of a soy bean !

@Woodbridge good points. Grade level slab - I think - the house is a reverse basement where most of the living space is upstairs but the main entry is downstairs. Not a split level. Front entry room, used like a family room it has a wood burning fireplace. Reasonably heavy traffic. Oh there are a few dings in the concrete where old carpet strips were once pulled up.
Thanks for all the replies thus far y'all.